Apparatus and method for full-diversity, full-rate space-time block coding for even number of transmit antennas

ABSTRACT

A mobile communication system using an STBC scheme having an even number of Tx antennas is provided. In a transmitter having an even number of Tx antennas, a pre-coder pre-codes an input symbol sequence using a pre-coding matrix. The pre-coding matrix is a matrix produced by puncturing a unitary matrix. A space-time coder space-time-encodes the pre-coded symbol sequence received from the pre-coder using a coding matrix.

This application claims priority under 35 U.S.C. § 119 to an applicationentitled “Apparatus And Method For Full-Diversity, Full-Rate Space-TimeBlock Coding For Even Number Of Transmit Antennas” filed in the KoreanIntellectual Property Office on Jun. 21, 2004 and assigned Serial No.2004-45924, the contents of which are herein incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to an apparatus and method forproviding transmit antenna diversity in a wireless communication system,and in particular, to an apparatus and method for space-time blockcoding (STBC) for an even number of transmit (Tx) antennas.

2. Description of the Related Art

Generally, in the wireless channel environment of a mobile communicationsystem, unlike that of a wired channel environment, a transmissionsignal inevitably experiences information loss due to several factorssuch as multipath interference, shadowing, wave attenuation,time-varying noise, and fading.

The resulting information loss can cause a severe distortion to theactual transmission signal, degrading the entire system performance. Inorder to reduce the information loss, many error control techniques areusually adopted depending on the characteristics of channels to increasesystem reliability. One common error control technique is an errorcorrection code method.

Multipath fading is reduced by diversity techniques in the wirelesscommunication system. The diversity techniques are classified into timediversity, frequency diversity, and antenna diversity.

The antenna diversity uses multiple antennas, and is further branchedinto a receive (Rx) antenna diversity using a plurality of Rx antennas,a Tx antenna diversity using a plurality of Tx antennas, and amultiple-input multiple-output (MIMO) using a plurality of Tx antennasand a plurality of Rx antennas.

The MIMO is a special case of space-time coding (STC) that extendscoding that exists in the time domain into the space domain by thetransmission of a signal encoded in a predetermined coding methodthrough a plurality of Tx antennas, with the aim to achieve a lowererror rate.

V. Tarokh, et al. proposed STBC as one of methods of efficientlyapplying the antenna diversity scheme (see “Space-Time Block Coding fromOrthogonal Designs”, IEEE Trans. On Info., Theory, Vol. 45, pp.1456-1467, July 1999). The Tarokh STBC scheme is an extension of thetransmit antenna diversity scheme of S. M. Alamouti (see, “A SimpleTransmit Diversity Technique for Wireless Communications”, IEEE Journalon Selected Area in Communications, Vol. 16, pp.1451-1458, October1988), for two or more Tx antennas.

FIG. 1 is a block diagram of a transmitter in a mobile communicationsystem using a conventional STBC. Proposed by Tarokh, the transmitter iscomprised of a modulator 100, a serial-to-parallel (S/P) converter 102,an STBC coder 104, and four Tx antennas 106, 108, 110 and 112.

Referring to FIG. 1, the modulator 100 modulates input information data(or coded data) according to a predetermined modulation scheme. Themodulation scheme can be one of binary phase shift keying (BPSK),quadrature phase shift keying (QPSK), quadrature amplitude modulation(QAM), and pulse amplitude modulation (PAM).

The S/P converter 102 parallel converts the serial modulation symbols(s₁, S₂, S₃, S₄) received from the modulator 100. The STBC coder 104creates eight symbol combinations by STBC-encoding the four modulationsymbols, S₁, S₂, S₃, S₄ and sequentially transmits them through the fourTx antennas 106 to 112. A coding matrix used to generate the eightsymbol combinations is expressed as $\begin{matrix}{G_{4} = \begin{bmatrix}s_{1} & s_{2} & s_{3} & s_{4} \\{- s_{2}} & s_{1} & {- s_{4}} & s_{3} \\{- s_{3}} & s_{4} & s_{1} & {- s_{2}} \\{- s_{4}} & {- s_{3}} & s_{2} & s_{1} \\s_{1}^{*} & s_{2}^{*} & s_{3}^{*} & s_{4}^{*} \\{- s_{2}^{*}} & s_{1}^{*} & {- s_{4}^{*}} & s_{3}^{*} \\{- s_{3}^{*}} & s_{4}^{*} & s_{1}^{*} & {- s_{2}^{*}} \\{- s_{4}^{*}} & {- s_{3}^{*}} & s_{2}^{*} & s_{1}^{*}\end{bmatrix}} & (1)\end{matrix}$where G₄ denotes the coding matrix for symbols transmitted through thefour Tx antennas 106 to 112 and S₁, S₂, S₃, S₄ denote the four inputsymbols to be transmitted. The number of the columns of the codingmatrix is equal to the number of the Tx antennas and the number of therows corresponds to the time required to transmit the four symbols.Thus, the four symbols are transmitted through the four Tx antennas overeight time intervals.

For a first time interval, si is transmitted through the first Txantenna 106, S₂ through the second Tx antenna 108, s₃ through the thirdTx antenna 110, and s₄ through the fourth Tx antenna 112. In thismanner, -s₄ ^(•), -s₃ ^(•), s₂ ^(•), -s₁ ^(•) are transmitted throughthe first to fourth Tx antennas 106 to 112, respectively for an eighthtime interval. The STBC coder 104 sequentially provides the symbols ofan ith column in the coding matrix to an ith Tx antenna.

As described above, the STBC coder 104 generates the eight symbolsequences using the input four symbols and their conjugates andnegatives and transmits them through the four Tx antennas 106 to 112 foreight time intervals. Since the symbol sequences for the respective Txantennas, that is, the columns of the coding matrix, are mutuallyorthogonal, a diversity gain as high as a diversity order is achieved.

FIG. 2 is a block diagram of a receiver in the mobile communicationsystem using the conventional STBC scheme. The receiver is thecounterpart of the transmitter illustrated in FIG. 1.

The receiver is comprised of a plurality of Rx antennas 200 to 202, achannel estimator 204, a signal combiner 206, a detector 208, aparallel-to-serial (P/S) converter 210, and a demodulator 212.

Referring to FIG. 2, the first to pth Rx antennas 200 to 202 providesignals received from the four Tx antennas of the transmitterillustrated in FIG. 1 to the channel estimator 204 and the signalcombiner 206.

The channel estimator 204 estimates channel coefficients representingchannel gains occurring between the Tx antennas 106 to 112 and the Rxantennas 200 to 202 using the signals received from the first to pth Rxantennas 200 to 202.

The signal combiner 206 combines the signals received from the first topth Rx antennas 200 to 202 with the channel coefficients.

The detector 208 generates hypothesis symbols by multiplying thecombined symbols by the channel coefficients, calculates decisionstatistics for all of the possible transmitted symbols from thetransmitter using the hypothesis symbols, and detects the actualtransmitted symbols through threshold detection.

The P/S converter 210 serial converts the parallel symbols received fromthe detector 208. The demodulator 212 demodulates the serial symbolsequence, thereby recovering the original information bits.

As stated earlier, the Alamouti STBC technique offers the benefit ofachieving a diversity order as high as the number of Tx antennas, namelya full diversity order, without sacrificing the data rate bytransmitting complex symbols through only two Tx antennas.

The Tarokh STBC scheme extended from the Alamouti STBC scheme achieves afull diversity order using an STBC in the form of a matrix withorthogonal columns, as described with reference to FIGS. 1 and 2.However, because four complex symbols are transmitted for eight timeintervals, the Tarokh STBC scheme brings about a decrease in the datarate by 50%. In addition, since it takes eight time intervals tocompletely transmit one block with four complex symbols, receptionperformance is degraded due to channel changes within the block over afast fading channel. In other words, the transmission of complex symbolsthrough four or more Tx antennas requires 2N time intervals for Nsymbols, causing a longer latency and a decrease in the data rate.

To achieve a full rate in a MIMO system that transmits a complex signalthrough three or more Tx antennas, the Giannakis group presented afull-diversity, full-rate (FDFR) STBC for four Tx antennas usingconstellation rotation over a complex field.

This FDFR STBC scheme will be described below.

FIG. 3 is a block diagram of a transmitter in a mobile communicationsystem using the conventional Giannakis STBC scheme. As illustrated inFIG. 3, the transmitter includes a modulator 300, a pre-coder 302, aspace-time mapper 304, and a plurality of Tx antennas 306, 308, 310 and312.

Referring to FIG. 3, the modulator 300 modulates input information data(or coded data) according to a predetermined modulation scheme such asBPSK, QPSK, QAM, PAM or PSK.

The pre-coder 302 pre-encodes Nt modulation symbols, d₁, d₂, d₃, d₄received from the modulator 300 such that signal rotation occurs in asignal space, and outputs the resulting N. symbols. For notationalsimplicity, four Tx antennas are assumed. Let a sequence of fourmodulation symbols from the modulator 300 be denoted by d. The pre-coder302 generates a complex vector r by computing the modulation symbolsequence, d using Equation (2). $\begin{matrix}{r = {{\Theta\quad d} = {{\begin{bmatrix}1 & \alpha_{0}^{1} & \alpha_{0}^{2} & \alpha_{0}^{3} \\1 & \alpha_{1}^{1} & \alpha_{1}^{2} & \alpha_{1}^{3} \\1 & \alpha_{2}^{1} & \alpha_{2}^{2} & \alpha_{2}^{3} \\1 & \alpha_{3}^{1} & \alpha_{3}^{2} & \alpha_{3}^{3}\end{bmatrix}\begin{bmatrix}d_{1} \\d_{2} \\d_{3} \\d_{4}\end{bmatrix}} = \begin{bmatrix}r_{1} \\r_{2} \\r_{3} \\r_{4}\end{bmatrix}}}} & (2)\end{matrix}$where Θ denotes a pre-coding matrix. The Giannakis group uses aVandermonde unitary matrix as the pre-coding matrix. In the pre-codingmatrix, α_(i) is given asα_(i)=exp(j2π(i+1/4)/4), i=0, 1, 2, 3  (3)

The Giannakis STBC scheme uses four Tx antennas and is easily extendedto more than four Tx antennas. The space-time mapper 304 STBC-encodesthe pre-coded symbols in the following method $\begin{matrix}{S = \begin{bmatrix}r_{1} & 0 & 0 & 0 \\0 & r_{2} & 0 & 0 \\0 & 0 & r_{3} & 0 \\0 & 0 & 0 & r_{4}\end{bmatrix}} & (4)\end{matrix}$where S is a coding matrix for symbols transmitted through the four Txantennas 306 to 312. The number of the columns of the coding matrix isequal to the number of Tx antennas, and the number of the rowscorresponds to the time required to transmit the four symbols. That is,the four symbols are transmitted through the four Tx antennas over fourtime intervals.

Specifically, for a first time interval, r₁ is transmitted through thefirst Tx antenna 306, with no signals being transmitted through theother Tx antennas 308, 310 and 312. For a second time interval, r₂ istransmitted through the second Tx antenna 308, with no signals beingtransmitted through the other Tx antennas 306, 310 and 312. For a thirdtime interval, r₃ is transmitted through the third Tx antenna 310, withno signals being transmitted through the other Tx antennas 306, 308, and312. For a fourth time interval, r₄ is transmitted through the fourth Txantenna 310, with no signals being transmitted through the other Txantennas 306, 308 and 310.

Upon receipt of the four symbols on a radio channel for the four timeintervals, a receiver (not shown) recovers the modulation symbolsequence, d by maximum likelihood (ML) decoding.

Taejin Jung and Kyungwhoon Cheun proposed a pre-coder and concatenatedcode with an excellent coding gain in 2003, compared to the GiannakisSTBC. They enhance the coding gain by concatenating Alamouti STBCsinstead of using a diagonal matrix proposed by the Giannakis group. Forconvenience sake, their STBC is referred to as “Alamouti FDFR STBC”.

The Alamouti FDFR STBC will be described below. FIG. 4 is a blockdiagram of a transmitter in a mobile communication system using theconventional Alamouti FDFR STBC for four Tx antennas As illustrated inFIG. 4, the transmitter includes a pre-coder 400, a mapper 402, a delay404, two Alamouti coders 406 and 408, and four Tx antennas 410, 412, 414and 416.

Referring to FIG. 4, the pre-coder 400 pre-encodes four input modulationsymbols, d₁, d₂, d₃, d₄ such that signal rotation occurs in a signalspace. For the input of a sequence of the four modulation symbols, d,the pre-coder 400 generates a complex vector, r by computing$\begin{matrix}{r = {{\Theta\quad d} = {{\begin{bmatrix}1 & \alpha_{0}^{1} & \alpha_{0}^{2} & \alpha_{0}^{3} \\1 & \alpha_{1}^{1} & \alpha_{1}^{2} & \alpha_{1}^{3} \\1 & \alpha_{2}^{1} & \alpha_{2}^{2} & \alpha_{2}^{3} \\1 & \alpha_{3}^{1} & \alpha_{3}^{2} & \alpha_{3}^{3}\end{bmatrix}\begin{bmatrix}d_{1} \\d_{2} \\d_{3} \\d_{4}\end{bmatrix}} = \begin{bmatrix}r_{1} \\r_{2} \\r_{3} \\r_{4}\end{bmatrix}}}} & (5)\end{matrix}$where α_(i)=exp(j2π(i+1/4)/4), i=0, 1, 2, 3.

The mapper 402 groups the four pre-coded symbols by twos and outputs twovectors each including two elements, [r₁, r₂]^(T) and [r₃, r₄]^(T) tothe Alamouti coder 406 and the delay 404, respectively.

The delay 404 delays the second vector [r₃, r₄]^(T) for one timeinterval. Thus, the first vector [r₁, r₂]^(T) is provided to theAlamouti coder 406 in a first time interval and the second vector [r₃,r₄]^(T) is provided to the Alamouti coder 408 in a second time interval.The Alamouti coder refers to a coder that operates in the Alamouti STBCscheme.

The Alamouti coder 406 encodes [r₁, r₂]^(T) so that it is transmittedthrough the first and second Tx antennas 410 and 412 at first and secondtime intervals. The Alamouti coder 408 encodes [r₃, r₄]^(T) so that itis transmitted through the third and fourth Tx antennas 414 and 416 atthird and fourth time intervals. A coding matrix used to transmit thefour symbols from the mapper 402 through the multiple antennas is$\begin{matrix}{S = \begin{bmatrix}r_{1} & r_{2} & 0 & 0 \\{- r_{2}^{*}} & r_{1}^{*} & 0 & 0 \\0 & 0 & r_{3} & r_{4} \\0 & 0 & {- r_{4}^{*}} & r_{3}^{*}\end{bmatrix}} & (6)\end{matrix}$

Unlike the coding matrix illustrated in Equation (4), the coding matrixof Equation (6) is designed to be an Alamouti STBC rather than adiagonal matrix. The use of the Alamouti STBC scheme increases thecoding gain.

This Alamouti FDFR STBC, however, has the distinctive shortcoming ofincreasing coding complexity because the transmitter needs to performcomputations between all of the elements of the pre-coding matrix and aninput vector, for pre-coding. For example, for four Tx antennas, since 0is not included in the elements of the pre-coding matrix, computationmust be carried out on 16 elements. Also, the receiver needs to performmaximum likelihood (ML) decoding with a large volume of computations inorder to decode the signal d transmitted by the transmitter.

Accordingly, a need exists for developing an FDFR STBC technique with aminimal complexity and a minimal computation volume.

SUMMARY OF THE INVENTION

An object of the present invention is to substantially solve at leastthe above problems and/or disadvantages and to provide at least theadvantages below. Accordingly, an object of the present invention is toprovide an apparatus and method for space-time block coding to achieve afull diversity gain and a full rate in a MIMO mobile communicationsystem.

Another object of the present invention is to provide an apparatus andmethod for space-time block coding to minimize coding and decodingcomplexities in a MIMO mobile communication system.

A further object of the present invention is to provide an apparatus andmethod for space-time block coding to achieve a full diversity gain anda full rate and to decrease coding and decoding complexities in a MIMOmobile communication system.

Still another object of the present invention is to provide an apparatusand method for space-time block coding to achieve a full diversity gainand a full rate and to decrease coding and decoding complexities in amobile communication system using an even number of Tx antennas.

Yet another object of the present invention is to provide an apparatusand method for space-time block coding for an even number of Tx antennasin a MIMO mobile communication system.

The above objects are achieved by providing a mobile communicationsystem using an STBC scheme with an even number of Tx antennas.

According to one aspect of the present invention, in a transmitter usingan even number of (Nt) Tx antennas, a pre-coder pre-codes an inputsymbol sequence using a pre-coding matrix. The pre-coding matrix is amatrix produced by puncturing a unitary matrix in a predeterminedmethod. A space-time coder space-time-encodes the pre-coded symbolsequence received from the pre-coder using a predetermined codingmatrix.

According to another aspect of the present invention, in a receiver in amobile communication system using a space-time coding scheme with aneven number of (N_(t)) Tx antennas, a matrix generator multiplies achannel response matrix H by a predetermined pre-coding matrix Θ andcalculates a Hermitian matrix (HΘ)^(H) of the product matrix. A signalcombiner calculates a vector of size N_(t) by multiplying a signalreceived through at least one receive antenna and the Hermitian matrix(HΘ)^(H) and divides the vector into two vectors.

According to a ftirther aspect of the present invention, in atransmission method in a transmitter using an even number of (N_(t))transmit antennas, an input symbol sequence is pre-coded using apre-coding matrix. The pre-coding matrix is a matrix produced bypuncturing a unitary matrix in a predetermined method. The pre-codedsymbol sequence is space-time-encoded using a predetermined codingmatrix.

According to still another aspect of the present invention, in areception method in a mobile communication system using a space-timecoding scheme with an even number of (N_(t)) transmit antennas, achannel response matrix H is multiplied by a predetermined pre-codingmatrix Θ and a Hermitian matrix (HΘ)^(H) of the product matrix iscalculated. A vector of size N_(t) is calculated by multiplying a signalreceived through at least one receive antenna and the Hermitian matrix(HΘ)^(H), and divided into two vectors. Symbols transmitted from atransmitter are estimated by decoding each of the two vectors receivedfrom the signal combiner in a predetermined decoding method.

According to yet another aspect of the present invention, in a method ofgenerating a pre-coding matrix in a system where transmission data ispre-coded and then space-time-encoded, a unitary matrix is generated,half of the columns of the unitary matrix are punctured, and thepre-coding matrix is generated by sequentially grouping the rows of thepunctured matrix by twos and shifting one row of each group.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will become more apparent from the following detaileddescription when taken in conjunction with the accompanying drawings inwhich:

FIG. 1 is a block diagram of a transmitter in a mobile communicationsystem using a conventional STBC scheme;

FIG. 2 is a block diagram of a receiver in the mobile communicationsystem using the conventional STBC scheme;

FIG. 3 is a block diagram of a transmitter in a mobile communicationsystem using a Giannakis STBC scheme;

FIG. 4 is a block diagram of a receiver in a mobile communication systemusing a Alamouti FDFR STBC scheme with four Tx antennas proposed byTaejin Jung and Kyungwhoon Cheun;

FIG. 5 is a block diagram of a transmitter in a MIMO mobilecommunication system using an STBC scheme for an even number of Txantennas according to an embodiment of the present invention;

FIG. 6 is a detailed block diagram of a pre-coding matrix generator in apre-coder according to the embodiment of the present invention;

FIG. 7 is a flowchart illustrating a transmission operation in thetransmitter illustrated in FIG. 5;

FIG. 8 is a block diagram of a receiver in the MIMO mobile communicationsystem using the STBC scheme for an even number of Tx antennas accordingto the embodiment of the present invention; and

FIG. 9 is a flowchart illustrating a reception operation in the receiverillustrated in FIG. 8.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

A preferred embodiment of the present invention will be described hereinbelow with reference to the accompanying drawings. In the followingdescription, well-known functions or constructions are not described indetail since they would obscure the invention in unnecessary detail.

The present invention is an apparatus and method for providing an FDFRSTBC with low coding and decoding complexities in a MIMO mobilecommunication system.

In accordance with the present invention, the FDFR STBC scheme is for aneven number of Tx antennas. A transmitter uses four Tx antennas asproposed by Taejin Jung and Kyungwhoon Cheun and is configured similarlyto a transmitter using an STBC. That is, the present invention proposesan Alamouti FDFR STBC that can extend the number of Tx antennas to 2N(N>1).

FIG. 5 is a block diagram of a transmitter in a MIMO mobilecommunication system using an STBC scheme for 2N (N>1) Tx antennasaccording to an embodiment of the present invention.

As illustrated, the transmitter includes a pre-coder 500, a mapper 502,a plurality of delays 504 to 506, a plurality of Alamouti coders 508 to512, and 2N (N>1) Tx antennas 514 to 524.

Referring to FIG. 5, information data is typically encoded in a coderand modulated in a modulator. The pre-coder 500 pre-encodes N_(t)modulation symbols, [d₁, d₂, . . . , d_(N) _(t) ] such that signalrotation takes place in a signal space and outputs a vector [r₁, r₂, . .. , r_(N) _(t) ] having N_(t) symbols. The pre-coder 500 encodes theinput symbols in a pre-coding matrix according to the present inventionand thus generates a complex vector, r. The pre-coding matrix will bedescribed later in great detail.

The mapper 502 groups the N. symbols into twos and outputs N_(t)/2vectors each having two elements, [r₁, r₂], [r₃, r₄], . . . , [r_(N)_(t) ₋₁, r_(N) _(t) ]. The first vector [r₁, r₂]^(T) is provided to theAlamouti coder 508 and the other vectors are provided to theirrespective corresponding delays 504 to 506.

The first delay 504 buffers the second vector [r₃, r₄]^(T) for one timeinterval and outputs it to the Alamouti coder 510. The second delay (notshown) buffers [r₅, r₆]^(T) for two time intervals and outputs it to thethird Alamouti coder (not shown). In the same manner, the(N_(t)/2-1)^(th) delay 506 buffers [r_(N) _(t) ₋₁, r_(N) _(t) ]^(T) for(N_(t)/2-1) time intervals and outputs it to the (N_(t)/2-1)^(th)Alamouti coder 512. Here, an Alamouti coder refers to a coder thatencodes in the Alamouti STBC scheme.

The Alamouti coder 508 encodes [r₁, r₂]^(T) so that it is transmittedthrough the first and second Tx antennas 514 and 516 for first andsecond time intervals. The Alamouti coder 510 encodes [r₃, r₄]^(T) sothat it is transmitted through the third and fourth Tx antennas 518 and520 for third and fourth time intervals. In the same manner, theAlamouti coder 512 encodes [r_(N) _(t) ₋₁, r_(N) _(t) ]^(T) so that itis transmitted through the (N_(t)-1)^(th) and N_(t) ^(th) Tx antennas522 and 524 for (N_(t)-1)^(th) and N_(t) ^(th) time intervals. Aplurality of antenna signals from the Alamouti coders 508 to 512 areprovided to their respective corresponding RF processors. The RFprocessors convert the input data to analog signals and modulate theanalog signals to RF signals for transmission over the air through theTx antennas 514 to 524.

Given N_(t) Tx antennas, a coding matrix used to transmit the output rof the pre-coder 500 through the multiple antennas is $\begin{matrix}{S = \begin{bmatrix}r_{1} & r_{2} & 0 & 0 & \cdots & 0 \\{- r_{2}^{*}} & r_{1}^{*} & 0 & 0 & \cdots & 0 \\0 & 0 & r_{3} & r_{4} & 0 & 0 \\0 & 0 & {- r_{4}^{*}} & r_{3}^{*} & 0 & 0 \\\vdots & \vdots & ⋰ & ⋰ & \vdots & \vdots \\0 & 0 & \cdots & \cdots & r_{N_{t} - 1} & r_{N_{t}} \\0 & 0 & \cdots & \cdots & {- r_{N_{t}}^{*}} & r_{N_{t} - 1}^{*}\end{bmatrix}} & (7)\end{matrix}$where an i^(th) row of the matrix S denotes transmission in an i^(th)time interval and a i^(th) column denotes transmission through a j^(th)Tx antenna. Specifically, r₁ and r₂ are transmitted through the firstand second Tx antennas 514 and 516, respectively for a first timeinterval. -r₂ ^(•) and r₁ ^(•) are transmitted through the first andsecond Tx antennas 514 and 516, respectively for a second time interval.In the same manner, r_(N) _(t) ₋₁and r_(N) _(t) are transmitted throughthe (N_(t)-1)^(th) and N_(t) ^(th) Tx antennas 522 and 524, respectivelyfor an (N_(t)-1)^(th) time interval. Finally, -r_(N) _(t) ^(•) and r_(N)_(t) ₋₁ ^(•) are transmitted through the (N_(t)-1)^(th) and N_(t) ^(th)Tx antennas 522 and 524, respectively for an N_(t) ^(th) time interval.

The operation of the pre-coder 500 illustrated in FIG. 5 will bedescribed below.

FIG. 6 is a detailed block diagram of a pre-coding matrix generator inthe pre-coder 500 according to the embodiment of the present invention.

As illustrated, the pre-coding matrix generator includes a matrixgenerator 600, a puncturer 602, and a shifter 604.

Referring to FIG. 6, the matrix generator 600 generates a Vandermondematrix according to the number of the Tx antennas. For Nt Tx antennas,an N_(t)×N_(t) Vandermonde matrix is generated.

The puncturer 602 punctures N_(t)/2 columns in the NtxNt Vandermondematrix. The puncturing is to substitute 0s for the elements of theN_(t)/2 columns.

The shifter 604 shifts even-numbered rows in the punctured Vandermondematrix, thereby moving non-punctured elements to the puncturedpositions. For the same effect, odd-numbered rows can be shifted, or therows are grouped into twos and one row of each group is shifted.

As described above, the pre-coding matrix is generated by puncturing of$\frac{N_{t} \times N_{t}}{2}$elements in the N_(t)×N_(t) matrix, thereby greatly reducing coding anddecoding complexities (computation volume) according to the presentinvention. While the pre-coder 500 generates the pre-coding matrix inthe above embodiment of the present invention, it can be furthercontemplated as another embodiment that a preliminarily generatedpre-coding matrix is stored in a memory and read for pre-coding by thepre-coder 500 when needed.

The operation of the pre-coding matrix generator is summarized asfollows.

(1) Generation of Vandermonde Matrix

An N_(t)×N_(t) Vandermonde matrix as shown below is generated. N_(t) isthe number of Tx antennas, as stated earlier. $\begin{matrix}{\Theta = \begin{bmatrix}1 & \alpha_{0}^{1} & \alpha_{0}^{2} & \cdots & \alpha_{0}^{N_{t} - 1} \\1 & \alpha_{1}^{1} & \alpha_{1}^{2} & \cdots & \alpha_{1}^{N_{t} - 1} \\\vdots & \vdots & ⋰ & \cdots & \vdots \\1 & \alpha_{N_{t} - 1}^{1} & \alpha_{N_{t} - 1}^{2} & \cdots & \alpha_{N_{t} - 1}^{N_{t} - 1}\end{bmatrix}} & (8)\end{matrix}$where α_(i)=exp(j2π(i+1/4)/N_(t)), i=0, 1, 2, . . . , N_(t)-1.

(2) Puncturing of Vandermonde Matrix $\frac{N_{t} \times N_{t}}{2}$elements are punctured in the N_(t)×N_(t) Vandermonde matrix byreplacing the $\frac{N_{t} \times N_{t}}{2}$elements with 0s. The resulting punctured matrix is $\begin{matrix}{\Theta = \begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & \cdots & 0 \\1 & \alpha_{1}^{1} & \cdots & \alpha_{1}^{{N_{t}/2} - 1} & 0 & \cdots & 0 \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots \\1 & \alpha_{N_{t} - 1}^{1} & \cdots & \alpha_{N_{t} - 1}^{{N_{t}/2} - 1} & 0 & \cdots & 0\end{bmatrix}} & (9)\end{matrix}$

(3) Shifting of Even-Numbered Rows in Punctured Matrix

A final pre-coding matrix is generated by shifting even-numbered rows inthe punctured N_(t)×N_(t) Vandermonde matrix. The shifting movesnon-punctured elements to punctured positions in the even-numbered rows.Thus, $\begin{matrix}{\Theta = \begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \cdots & \alpha_{1}^{{N_{t}/2} - 1} \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots \\1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1} & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \cdots & \alpha_{N_{t} - 1}^{{N_{t}/2} - 1}\end{bmatrix}} & (10)\end{matrix}$Even if α_(i) is set such that α₀=α₁, α₂=α₃, and α_(N) _(t) ₋₂=α_(N)_(t) ₋₁, there is no change in performance. Instead of the even-numberedrows, the odd-numbered rows can be shifted, resulting in the sameeffect.

As described above, for Nt Tx antennas, the operation of the pre-coder500 is implemented by $\begin{matrix}\begin{matrix}{{N_{t}r} = {\Theta\quad d}} \\{= {\begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots & \vdots \\1 & \alpha_{{N_{t}/2} - 1}^{1} & \cdots & \alpha_{{N_{t}/2} - 1}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{{N_{t}/2} - 1}^{1} & \cdots & \alpha_{{N_{t}/2} - 1}^{{N_{t}/2} - 1}\end{bmatrix}\begin{bmatrix}d_{1} \\d_{2} \\\vdots \\d_{N_{t} - 1} \\d_{N_{t}}\end{bmatrix}}} \\{= \begin{bmatrix}r_{1} \\r_{2} \\\vdots \\r_{N_{t} - 1} \\r_{N_{t}}\end{bmatrix}}\end{matrix} & (11)\end{matrix}$where [d₁, d₂, . . . , d_(N) _(t) ₋₁, d_(N) _(t) ] is an input symbolsequence to the pre-coder 500 and [r₁, r₂, . . . , r_(N) _(t) ₋₁, r_(N)_(t) ] is an output symbol sequence from the pre-coder 500.

The elements of the thus-designed pre-coding matrix E) must be optimizedto maximize the coding gain. This is done by mathematical computationsor simulation.

In accordance with the embodiment of the present invention, pre-codingmatrices (D with a maximum coding gain are achieved by simulation. Thesepre-coding matrices are illustrated below.

For an Alamouti FDFR STBC system with four antennas, the followingpre-coding matrix Θ is available. $\begin{matrix}{\Theta = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} \\1 & {\mathbb{e}}^{{- j}\quad\theta_{1}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{1}}\end{bmatrix}}} & (12)\end{matrix}$where 0≦θ₀, θ₁≦2π, and |θ₁-θ₂|=180°.

For an Alamouti FDFR STBC system with six antennas, the followingpre-coding matrix Θ is available. $\begin{matrix}{\Theta = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi}\end{bmatrix}}} & (13)\end{matrix}$

For an Alamouti FDFR STBC system with eight or more antennas, thefollowing pre-coding matrix Θ is available. $\begin{matrix}{\Theta = {\frac{1}{\sqrt{N_{t}/2}}\begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots & \vdots \\1 & \alpha_{{N_{t}/2} - 1}^{1} & \cdots & \alpha_{{N_{t}/2} - 1}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{{N_{t}/2} - 1}^{1} & \cdots & \alpha_{{N_{t}/2} - 1}^{{N_{t}/2} - 1}\end{bmatrix}}} & (14)\end{matrix}$α_(i)=exp(j2π(i+1/4)/N_(t)), i=0, 1, 2, . . . , N_(t)/2-1.

Now a description will be made of the operation of the transmitterillustrated in FIG. 5.

FIG. 7 is a flowchart illustrating the transmitter in the MIMO mobilecommunication system using the STBC scheme for 2N (N>1) Tx antennasaccording to the embodiment of the present invention.

Referring to FIG. 7, the transmitter receives a data stream to betransmitted, d ([d₁, d₂, . . . , d_(N) _(t) ₋₁, d_(N) _(t) ]) in step700. d can be a coded and modulated complex symbol sequence. In step702, the transmitter generates a pre-coded symbol sequence r ([r₁, d₂, .. . , r_(N) _(t) ₋₁, r_(N) _(t) ]) by encoding the input data streamusing a predetermined pre-coding matrix Θ. Θ is created by puncturingone half of a Vandermonde matrix and shifting rows, as describedearlier. Due to the half-puncturing, the pre-coding matrix significantlyreduces coding and decoding complexities.

In step 704, the transmitter groups the symbols of the sequence r bytwos and performs space-time mapping on the grouped symbols.Specifically, N. symbols are grouped into N_(t)/2 vectors each havingtwo elements.

The transmitter then sets a time index i to an initial value of 0 instep 706, and compares i with N_(t) (the number of Tx antennas) in step708. If i is less than N_(t), the transmitter receives a vector havingi^(th) and (i+1)^(th) symbols of the pre-coded symbol sequence, r instep 710.

In step 712, the transmitter delays the received vector for i/2 timeintervals. Therefore, an initial input, that is, the first and secondsymbols are transmitted through two Tx antennas with no time delay. Thefollowing symbols are delayed and then transmitted through correspondingTx antennas.

After the time delay, the transmitter encodes the received vector withtwo symbols in the Alamouti STBC scheme and transmits the coded vectorthrough two Tx antennas in step 714. Specifically, a plurality ofSTBC-coded antenna signals are modulated to RF signals and transmittedthrough their corresponding antennas.

In step 716, the transmitter increases i by two, and returns to step708.

If i is equal to or greater than N_(t) in step 708, the transmitterterminates the algorithm, determining that the transmission data hasbeen completely transmitted.

FIG. 8 is a block diagram of a receiver in the MIMO mobile communicationsystem using the STBC scheme for 2N (N>1) Tx antennas according to theembodiment of the present invention. The receiver shown in FIG. 8 is thecounter part of the transmitter illustrated in FIG. 5.

As illustrated in FIG. 8, the receiver includes P Rx antennas 800 to804, a channel estimator 806, a (HΘ)^(H) generator 808, a signalcombiner 810, and two signal deciders 812 and 814. While the embodimentof the present invention is described under the presumption that thenumber of Tx antennas in the transmitter is different from that of Rxantennas in the receiver, the number of Tx and Rx antennas can be thesame.

Referring to FIG. 8, signals transmitted from the Tx antennas 514 to 524in FIG. 5 in the transmitter arrive at the first to P^(th) Rx antennas800 to 804. Typically, the received signals are downconverted tobaseband signals by an RF processor and provided to the channelestimator 806 and the signal combiner 810.

The channel estimator 806 estimates channel coefficients representingchannel gains from the received signals. The (HΘ)^(H) generator 808constructs a channel response matrix H with the channel coefficients andcalculates a Hermitian matrix (HΘ)^(H) by multiplying the channelresponse matrix H by a known pre-coding matrix Θ.

The signal combiner 810 generates a received symbol sequence bymultiplying the signals received from the first to pth Rx antennas 800to 804 by the Hermitian matrix (HΘ)^(H). First to (N_(t)/2)^(th) symbolsin the symbol sequence are provided to the first signal decider 812, and(N_(t)/2+1)^(th) to N_(t) ^(th) symbols are provided to the secondsignal decider 814.

The signal decider 812 estimates symbols transmitted by the transmitterby performing, for example, ML decoding on the vector of size N_(t)/2received from the signal combiner 810 and outputs the estimated symbols,{tilde over (d)}₁, {tilde over (d)}₂, . . . , {tilde over (d)}_(N) _(t)_(/2). The signal decider 814 estimates symbols transmitted by thetransmitter by performing, for example, ML decoding on the vector ofsize N_(t)/2 received from the signal combiner 810 and outputs theestimated symbols, {tilde over (d)}_(N) _(t) _(/2+1), {tilde over(d)}_(N) _(t) _(/2+2), . . . , {tilde over (d)}_(N) _(t) . The operationof the signal deciders 812 and 814 are implemented by Equation (17). Theestimated symbols are demodulated in a demodulator and recovered to theoriginal information data in a decoder.

The ML decoding for size N_(t)/2 considerably reduces computationvolume, compared to an existing ML decoding for size N_(t).

The operation of the receiver is summarized in mathematical terms asfollows.

For one Rx antenna for example, the received signal isy=Hr=HΘd+nwhere y=[y₁y₂ ^(•) . . . y_(N) _(t) ₋₁y_(N) _(t) ^(•)]^(T). That is, yis a vector that includes signals received for N_(t) time intervals, y₁,y₂, . . . y_(N) _(t) ₋₁, y_(N) _(t) and their conjugates. Thus, thevector y is multiplied by (HΘ)^(H) to estimate a signal transmitted fromthe transmitter, d=[d₁, d₂, . . . , d_(N) _(t) ₋₁, d_(N) _(t) ]^(T).This operation is expressed as $\begin{matrix}\begin{matrix}{y^{\prime} = {( {H\quad\Theta} )^{H}\quad y}} \\{= {{( {H\quad\Theta} )^{H}\quad H\quad\Theta\quad d} + {( {H\quad\Theta} )^{H}\quad n}}} \\{= {{\begin{bmatrix}A & 0 \\0 & A\end{bmatrix}\begin{bmatrix}d_{1} \\d_{2} \\\vdots \\d_{N_{t} - 1} \\d_{N_{t}}\end{bmatrix}} + {( {H\quad\Theta} )^{H}\begin{bmatrix}n_{1}^{\prime} \\n_{2}^{\prime*} \\n_{3}^{\prime} \\\vdots \\n_{N_{t} - 1}^{\prime} \\n_{N_{t}}^{\prime*}\end{bmatrix}}}}\end{matrix} & (16)\end{matrix}$where A denotes a $\frac{N_{t}}{2} \times \frac{N_{t}}{2}$matrix.

Equation (16) reveals that the resulting vector can be divided into twovectors of size N_(t)/2 (d₁, d₂, . . . ,d_(N) _(t) _(/2)) and (d_(N)_(t) ₂₊₁, d_(N) _(t) ₂₊₂, . . . , d_(N) _(t) ), and ML decoding can beperformed on each of the two vectors.

The signal transmitted by the transmitter is determined by$\begin{matrix}\begin{matrix}{{\overset{\sim}{d}}_{1,2,\quad\ldots\quad,{N_{t}/2}} = {\arg_{d_{1,2,\quad\ldots\quad,{N_{t}/2}}}^{\min}{{y_{1,2,\quad\ldots\quad,{N_{t}/2}}^{\prime} - {A\quad d_{1,2,\quad\ldots\quad,{N_{t}/2}}}}}^{2}}} \\{{\overset{\sim}{d}}_{{{N_{t}/2} + 1},\quad\ldots\quad,N_{t}} = {\arg_{d_{{{N_{t}/2} + 1},\quad\ldots\quad,N_{t}}}^{\min}{{y_{{{N_{t}/2} + 1},\quad\ldots\quad,N_{t}}^{\prime} - {A\quad d_{{{N_{t}/2} + 1},\quad\ldots\quad,N_{t}}}}}^{2}}}\end{matrix} & (17)\end{matrix}$where {tilde over (d)}_(1,2, . . . , N) _(t) _(/2)=[{tilde over (d)}₁, .. . , {tilde over (d)}N_(t) _(t) _(/2)], {tilde over (d)}_(N) _(t)_(/2+1, . . . , N) _(t) =[{tilde over (d)}_(N) _(t) _(/2+1), . . . ,{tilde over (d)}_(N) _(t) ], d_(1,2, . . . , N) _(t) _(/2)=[d₁, . . . ,d_(N) _(t) _(/2)], d_(N) _(t) _(/2+1, . . . , N) _(t) =[d_(N) _(t)_(/2+1), . . . , d_(N) _(t) ], y′_(1,2, . . . , N) _(t) _(/2)=[y′₁, . .. , y′_(N) _(t) _(/2)], and y′_(N) _(t) _(/2+1, . . . , N) _(t) =[y′_(N)_(t) _(/2+1), . . . , y′_(N) _(t) ]. That is, for an even number of(N_(t)) Tx antennas, Alamouti FDFR STBC decoding is carried out byML-decoding vectors each having N_(t)/2 elements.

The operation of the receiver illustrated in FIG. 8 will be describedbelow.

FIG. 9 is a flowchart illustrating a reception operation in the receiverin the MIMO mobile communication system using the STBC scheme for 2N(N>1) Tx antennas according to the embodiment of the present invention.

Referring to FIG. 9, the receiver calculates channel coefficientsrepresenting channel gains between the transmitter and the receiverusing a signal y received through the Rx antennas in step 900.

In step 902, the receiver generates a channel response matrix H usingthe estimated channel coefficients and produces a Hermitian matrix,(HΘ)^(H) by multiplying the channel response matrix H by the pre-codingmatrix Θ.

The receiver generates a vector having Nt elements by multiplying theHermitian matrix (HΘ)^(H) by the received signal y in step 904. In step906, the receiver divides the vector into two vectors and ML-decodeseach of the two vectors, thereby deciding symbols transmitted from thetransmitter. These symbols are recovered to the original informationdata through demodulation and decoding.

In a comparison between a conventional STBC scheme and the STBC schemeof the present invention in terms of decoding complexity, for ₂m complexsignals, a pre-coder in the Alamouti FDFR STBC of Taejin Jung andKyungwhoon Cheun has a decoding complexity of (2^(m))⁴, while thepre-coder of the present invention has a far less decoding complexity of2×(2^(m))².

For 16QAM, for instance, the decoding complexity is C_(old)=(2⁴)⁴=2¹⁶ inthe conventional pre-coder and C_(new)=2(2⁴)²=2⁹ in the pre-coder of thepresent invention. Thus, ${\frac{C_{new}}{C_{old}} = 0.0078},$which implies that the present invention considerably decreasescomputation volume.

It is concluded that compared to the Alamouti FDFR STBC scheme, theinventive STBC scheme achieves almost the same performance and yetminimizes the computation volume and complexity.

As described above, the efficient STBC coding and decoding algorithms ofthe present invention enable the implementation of a high-reliabilitycommunication system. Compared to the conventional FDFR STBC schemeusing a pre-coder, the STBC scheme of the present invention greatlyreduces decoding complexity, ensuring excellent performance.

While the invention has been shown and described with reference to acertain preferred embodiment thereof, it will be understood by thoseskilled in the art that various changes in form and details may be madetherein without departing from the spirit and scope of the invention asdefined by the appended claims.

1. A transmitter having an even number of (N_(t)) transmit antennas,comprising: a pre-coder for pre-coding an input symbol sequence using apre-coding matrix, the pre-coding matrix produced by puncturing aunitary matrix; and a space-time coder for space-time-encoding thepre-coded symbol sequence received from the pre-coder using a codingmatrix.
 2. The transmitter of claim 1, wherein the space-time codercomprises: a mapper for generating a plurality of vectors by groupingthe symbols of the pre-coded symbol sequence by twos; and a plurality ofcoders for encoding each of the vectors in an Alamouti coding scheme andtransmitting each of the coded vectors through two antennas.
 3. Thetransmitter of claim 2, wherein an i^(th) coder from among the pluralityof coders encodes an i^(th) vector in the Alamouti coding scheme andtransmits the coded vector through two antennas for (2i-1)^(th) and2i^(th) time intervals, where i=1, 2, 3, . . . , N_(t)/2.
 4. Thetransmitter of claim 1, wherein the coding matrix is$S = \begin{bmatrix}r_{1} & r_{2} & 0 & 0 & \cdots & 0 \\{- r_{2}^{*}} & r_{1}^{*} & 0 & 0 & \cdots & 0 \\0 & 0 & r_{3} & r_{4} & 0 & 0 \\0 & 0 & {- r_{4}^{*}} & r_{3}^{*} & 0 & 0 \\\vdots & \vdots & ⋰ & ⋰ & \vdots & \vdots \\0 & 0 & \cdots & \cdots & r_{N_{t} - 1} & r_{N_{t}} \\0 & 0 & \cdots & \cdots & {- r_{N_{t}}^{*}} & r_{N_{t} - 1}^{*}\end{bmatrix}$ where r₁, r₂, . . . , r_(N) _(t) is a symbol sequenceoutput from the pre-coder, an i^(th) row in the matrix S denotestransmission in an i^(th) time interval, and a j^(th) column denotestransmission through a j^(th) Tx antenna.
 5. The transmitter of claim 1,wherein the pre-coding matrix is produced by puncturing N_(t)/2 columnsin an N_(t)×N_(t) Vandermonde matrix, sequentially grouping the rows ofthe punctured matrix by twos, and shifting one row of each group.
 6. Thetransmitter of claim 1, wherein if the number of transmit antennas is 4(N_(t)=4), the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} \\1 & {\mathbb{e}}^{{- j}\quad\theta_{1}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{1}}\end{bmatrix}}$ where 0≦θ₀, θ₁≦2π, and |θ₁-θ₂|=180°.
 7. The transmitterof claim 1, wherein if the number of transmit antennas is 6 (N_(t)=6),the pre-coding matrix is $\Theta = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi}\end{bmatrix}}$
 8. The transmitter of claim 1, wherein for the evennumber of transmit antennas (N_(t)=even number), the pre-coding matrixis $\Theta = {\frac{1}{\sqrt{N_{t}/2}}\begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots & \vdots \\1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1}\end{bmatrix}}$ where α_(i)=exp(j2π(i+1/4)/N_(t)), i=0, 1, 2, . . . ,N_(t)/2-1.
 9. The transmitter of claim 1, further comprising: a coderfor encoding transmission data; a modulator for modulating the codedsymbols received from the coder and providing the modulated symbols tothe pre-coder; and a radio frequency (RF) modulator for modulating theplurality of antenna signals received form the space-time coder to RFsignals and outputting the RF signals to antennas.
 10. A pre-codingmatrix generator in a system where transmission data is pre-coded andthen space-time-encoded, comprising: a matrix generator for generating aunitary matrix; a puncturer for puncturing half the columns of theunitary matrix; and a shifter for generating a pre-coding matrix bysequentially grouping the rows of the punctured matrix by twos andshifting one row of each group.
 11. The pre-coding matrix generator ofclaim 10, wherein the unitary matrix is a Vandermonde matrix.
 12. Thepre-coding matrix generator of claim 10, wherein for four transmitantennas, the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} \\1 & {\mathbb{e}}^{{- j}\quad\theta_{1}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{1}}\end{bmatrix}}$ where 0≦θ₀, θ₁≦2π, and |θ₁-θ₂|=180°.
 13. The apparatusof claim 10, wherein for six transmit antennas, the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi}\end{bmatrix}}$
 14. The apparatus of claim 10, wherein for N_(t)transmit antennas, the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{N_{t}/2}}\begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots & \vdots \\1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1}\end{bmatrix}}$ where α_(i)=exp(j2π(i+1/4)/N_(t)), i=0, 1, 2, . . . ,N_(t)/2-1.
 15. A receiver in a mobile communication system using aspace-time coding scheme with an even number of (N_(t)) transmitantennas, comprising: a matrix generator for multiplying a channelresponse matrix H by a pre-coding matrix Θ and calculating a Hermitianmatrix (HΘ)^(H) of the product matrix; and a signal combiner forcalculating a vector of size N_(t) by multiplying a signal receivedthrough at least one receive antenna and the Hermitian matrix (HΘ)^(H),and dividing the vector into two vectors.
 16. The receiver of claim 15,further comprising a signal decider for estimating symbols transmittedfrom a transmitter by decoding each of the two vectors received from thesignal combiner according to a decoding method.
 17. The receiver ofclaim 15, wherein the decoding method is maximum likelihood (ML)decoding.
 18. The receiver of claim 15, wherein the pre-coding matrix isproduced by puncturing N_(t)/2 columns in an N_(t)×N_(t) Vandermondematrix, sequentially grouping the rows of the punctured matrix by twos,and shifting one row of each group.
 19. The receiver of claim 15,wherein if the number of transmit antennas is 4 (N_(t)=4), thepre-coding matrix is $\Theta = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} \\1 & {\mathbb{e}}^{{- j}\quad\theta_{1}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{1}}\end{bmatrix}}$ where 0≦θ₀, θ₁≦2π, and |θ₁-θ₂|=180°.
 20. The receiver ofclaim 15, wherein if the number of transmit antennas is 6 (N_(t)=6), thepre-coding matrix is $\Theta = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi}\end{bmatrix}}$
 21. The receiver of claim 15, wherein for an even numberof transmit antennas (N_(t)=even number), the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{N_{t}/2}}\begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots & \vdots \\1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1}\end{bmatrix}}$ where α_(i)=exp(j2π(i+1/4)/N_(t)), i=0, 1, 2, . . . ,N_(t)/2-1.
 22. The receiver of claim 16, further comprising: a radiofrequency (RF) processor for downconverting the signal received throughthe at least one receive antenna to a baseband signal and providing thebaseband signal to a channel estimator and the signal combiner; thechannel estimator for calculating the channel response matrix H usingthe baseband signal; a demodulator for demodulating the estimatedsymbols received from the signal decider; and a decoder for decoding thedemodulated symbols received form the demodulator.
 23. A transmissionmethod in a transmitter using an even number of (N_(t)) transmitantennas, comprising the steps of: pre-coding an input symbol sequenceusing a pre-coding matrix, the pre-coding matrix being produced bypuncturing a unitary matrix; and space-time-encoding the pre-codedsymbol sequence using a coding matrix.
 24. The transmission method ofclaim 23, wherein the space-time-encoding step comprises the steps of:generating a plurality of vectors by grouping the symbols of thepre-coded symbol sequence by twos; and encoding each of the vectors inan Alamouti coding scheme and transmitting each of the coded vectorsthrough two antennas.
 25. The transmission method of claim 24, whereinthe encoding and transmitting step comprises the step of encodingani^(th) vector from among the plurality of vectors in the Alamouticoding scheme and transmitting the coded vector through two antennas for(2i-1)^(th) and 2i^(th) time intervals, where i=1, 2, 3, . . . ,N_(t)/2.
 26. The transmission method of claim 23, wherein the codingmatrix is given by is $S = \begin{bmatrix}r_{1} & r_{2} & 0 & 0 & \cdots & 0 \\{- r_{2}^{*}} & r_{1}^{*} & 0 & 0 & \cdots & 0 \\0 & 0 & r_{3} & r_{4} & 0 & 0 \\0 & 0 & {- r_{4}^{*}} & r_{3}^{*} & 0 & 0 \\\vdots & \vdots & ⋰ & ⋰ & \vdots & \vdots \\0 & 0 & \cdots & \cdots & r_{N_{t} - 1} & r_{N_{t}} \\0 & 0 & \cdots & \cdots & {- r_{N_{t}}^{*}} & r_{N_{t} - 1}^{*}\end{bmatrix}$ where r₁, r₂, . . . , r_(N) _(t) is a pre-coded symbolsequence, an i^(th) row in the matrix S denotes transmission in ani^(th) time interval, and a j^(th) column denotes transmission through aj^(th) Tx antenna.
 27. The transmission method of claim 23, wherein thepre-coding matrix is produced by puncturing N_(t)/2 columns in anN_(t)×N_(t) Vandermonde matrix, sequentially grouping the rows of thepunctured matrix by twos, and shifting one row of each group.
 28. Thetransmission method of claim 23, wherein if the number of transmitantennas is 4 (N_(t)=4), the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} \\1 & {\mathbb{e}}^{{- j}\quad\theta_{1}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{1}}\end{bmatrix}}$ where 0≦θ₀, θ₁≦2π, and |θ₁-θ₂|=180°.
 29. Thetransmission method of claim 23, wherein if the number of transmitantennas is 6 (N_(t)=6), the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi}\end{bmatrix}}$
 30. The transmission method of claim 23, wherein for aneven number of transmit antennas (N_(t)=even number), the pre-codingmatrix is $\Theta = {\frac{1}{\sqrt{N_{t}/2}}\begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots & \vdots \\1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1}\end{bmatrix}}$ where α_(i)=exp(j2π(i+1/4)/N_(t)), i=0, 1, 2, . . . ,N_(t)/2-1.
 31. The transmission method of claim 23, further comprisingthe steps of: generating coded symbols by encoding transmission data;modulating the coded symbols and providing the modulated symbols forpre-coding; and modulating a plurality of antenna signals generated byspace-time encoding to radio frequency (RF) signals and transmitting theRF signals.
 32. A method of generating a pre-coding matrix in a systemwhere transmission data is pre-coded and then space-time-encoded,comprising the steps of: generating a unitary matrix; puncturing halfthe columns of the unitary matrix; and generating the pre-coding matrixby sequentially grouping the rows of the punctured matrix by twos andshifting one row of each group.
 33. The method of claim 32, wherein theunitary matrix is a Vandermonde matrix.
 34. The method of claim 32,wherein for four transmit antennas, the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} \\1 & {\mathbb{e}}^{{- j}\quad\theta_{1}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{1}}\end{bmatrix}}$ where 0≦θ₀, θ₁≦2π, and |θ₁-θ₂|=180°.
 35. The method ofclaim 32, wherein for six transmit antennas, the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi}\end{bmatrix}}$
 36. The method of claim 32, wherein for N_(t) transmitantennas, the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{N_{t}/2}}\begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots & \vdots \\1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1}\end{bmatrix}}$ where α_(i)=exp(j2π(i+1/4)/N_(t)), i=0, 1, 2, . . . ,N_(t)/2-1.
 37. A reception method in a mobile communication system usinga space-time coding scheme with an even number of (N_(t)) transmitantennas, comprising the steps of: multiplying a channel response matrixH by a pre-coding matrix Θ and calculating a Hermitian matrix (HΘ)^(H)of the product matrix; calculating a vector of size N_(t) by multiplyinga signal received through at least one receive antenna and the Hermitianmatrix (HΘ)^(H) and dividing the vector into two vectors; and estimatingsymbols transmitted from a transmitter by decoding each of the twovectors received from the signal combiner according to a decodingmethod.
 38. The reception method of claim 37, wherein the decodingmethod is maximum likelihood (ML) decoding.
 39. The reception method ofclaim 37, wherein the pre-coding matrix is produced by puncturingN_(t)/2 columns in an N_(t)×N_(t) Vandermonde matrix, sequentiallygrouping the rows of the punctured matrix by twos, and shifting one rowof each group.
 40. The reception method of claim 37, wherein if thenumber of transmit antennas is 4 (N_(t)=4), the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{2}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{0}} \\1 & {\mathbb{e}}^{{- j}\quad\theta_{1}} & 0 & 0 \\0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\theta_{1}}\end{bmatrix}}$ where 0≦θ₀, θ₁≦2π, and |θ₁-θ₂|=180°.
 41. The receptionmethod of claim 37, wherein if the number of transmit antennas is 6(N_(t)=6), the pre-coding matrix is$\Theta = {\frac{1}{\sqrt{3}}\begin{bmatrix}1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{5}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{10}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{11}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{4}{9}\pi} \\1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi} & 0 & 0 & 0 \\0 & 0 & 0 & 1 & {\mathbb{e}}^{{- j}\quad\frac{17}{9}\pi} & {\mathbb{e}}^{{- j}\quad\frac{16}{9}\pi}\end{bmatrix}}$
 42. The reception method of claim 37, wherein for aneven number of transmit antennas (N_(t)even number), the pre-coddingmatrix is $\Theta = {\frac{1}{\sqrt{N_{t}/2}}\begin{bmatrix}1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{0}^{1} & \cdots & \alpha_{0}^{{N_{t}/2} - 1} \\\vdots & \vdots & ⋰ & \cdots & \cdots & ⋰ & \vdots & \vdots \\1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1} & 0 & 0 & \cdots & 0 \\0 & 0 & \cdots & 0 & 1 & \alpha_{N_{t} - 2}^{1} & \cdots & \alpha_{N_{t} - 2}^{{N_{t}/2} - 1}\end{bmatrix}}$ where α_(i)=exp(j2π(i+1/4)/N_(t)), i=0, 1, 2, . . . ,N_(t)/2-1.
 43. The reception method of claim 37, further comprising thesteps of: calculating the channel response matrix, H using the signalreceived through the at least one antenna; demodulating the estimatedsymbols; and recovering original information data by decoding thedemodulated symbols.